Bowyer dominated Sunday's race, but defending race winner Busch was all over his bumper late.
A caution with four laps remaining set up a final restart and overtime finish, and forced Bowyer to earn the victory. He raced side-by-side with Busch at the green flag, but cleared Busch and pulled away for the win.
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Although Bowyer finished fourth three previous times on this road course, his background is on dirt tracks and this style of racing isn't his strong suit.
"To have this dirt boy from Kansas at Victory Lane on a road course is big, trust me," Bowyer said. "I saw Jeff Gordon, he's sitting there on the wall, he's won this race many times, he's a champion of this sport and I just beat him. I passed Jeff Gordon, and you have no idea, a young racer from Kansas, you don't forget stuff like that."
Bowyer dominated by leading 71 of the 112 laps. Busch, in an unsponsored car, was all over the bumper of Bowyer's Toyota late and got a final shot at taking the win away when caution flew with four laps remaining.
Only Busch damaged his car with roughly eight laps to go, and he worried the entire caution period whether his Chevrolet was ruined and had no chance of catching Bowyer through the two-lap overtime sprint to the finish.
Bowyer raced side-by-side with Busch at the green flag, then cleared Busch and pulled away for the win.
"Kurt raced me clean, he bumped me and roughed me up, but never did anything to jeopardize either one of us," Bowyer said.
Bowyer, who left Richard Childress Racing at the end of last season to join MWR, had to walk to Victory Lane to celebrate with his new crew after his car ran out of fuel.
"I'm super excited for everybody involved," Bowyer said. "To switch teams like I did was a huge risk and a chance for me, and it was a chance to showcase my talents.
"I've had good teammates and good stuff before, but never like this. This is a young group, Michael stuck it out and I'm telling you, he's fixing to reap the benefits. He's worked hard."
It was a strong day all-around for MWR, which got a fourth-place finish from Brian Vickers, who was back to NASCAR after racing last weekend at Le Mans. Martin Truex Jr. led 15 laps, and was running in the top 10 until a late-race incident dropped him to 22nd.
"Everybody is just working together," Bowyer said. "That's something we are very proud of."
Tony Stewart passed Busch on the final lap to claim second, but said it was because Busch's car was struggling.
"Every time he would go in the corner, the rear end would shift, and it was running him to the outside of the track on entry and it was screwing his corner up," Stewart said. "Kind of got it by default there to a certain degree. Once we got by there, we just were not close enough in that last lap to get to Clint."
Busch finished third. He was emotional after -- Busch missed Pocono earlier this month because he was suspended by NASCAR for verbally abusing a media member -- and said he was thrilled to compete for the win in an underfunded, unsponsored Phoenix Racing car.
"It's an amazing day, when you can do what we did," Busch said. "I'm a little choked up because A: We were in position. B: I was very considerate to Bowyer, who was going for his first win with the new team. And then C: which is most important, I made a mistake, I got into those tires in turn 11."
Busch, who has struggled with his temper on and off the track, saw a silver lining in his strong finish.
"If I can get my head on straight here, and after the race, then I could be able to race every weekend and go for victories," Busch said.
Most everyone believed the race would be a runaway win for either Ambrose or Gordon, but neither really contended.